Wouldn't work. Taxes will not do it. What would work is draconian but would definitely work.
1. Stop the wiring home of money from the USA to Mexico.
2. Prohibit children of illegals from getting a free education.
3. Stop giving babies of illegals citizenship.
4. Establish citizenship and residency requirements for receipt of all federal benefits such as social security, Medicare and Medicaid, neonatal care, etc.
5. Pass federal legislation requiring all state and local peace officers, plus other state and local goverment officials, requiring them to inquire of legal status when they encounter someone; also provide the funding to detain and incarcerate those illegals detected this way.
6. Pass federal legislation requiring (5) for hospitals and schools, otherwise the institutions receive no federal funding or subsidy.
7. Pass legislation that requires incarceration and significant fines for breaking immigration laws, but include liberal rules for suspending them for the first infraction. E.g., 30 days plus $1,000 for the first offense. For subsequent offenses, the penalty becomes punitive, e.g., 6 months and $10,000. So the second time the feds start seizing cars and attaching funds in bank accounts.
This would stop illegals. You don't need to hunt them down. When they emerge, they will eventually be detected. And everything is done humanely and with human dignity.
[...What would work is draconian but would definitely work...]
These ideas are great. If you aren't running for senate or congress on these planks, share with with a representative who will.